Ice is the greatsword of House Stark made from Valyrian steel. Eddard Stark uses it in the first episode to behead a deserter of the Nightswatch. At the end of season 1 Ser Illyn Payne uses the sword to execute Eddard Stark.
The White Walker in the first episode uses a sword with a blade made from ice to kill two of the three rangers.
Needle is the sword Jon Snow gives to his halfsister Arya Stark before departing to the Nightswatch. Being very light and tiny it was forged especially for her.
Hill tribe axesEdit
Some of the hill tribe warriors attacking Caitlyn Stark and her party in the hills of the Vale carry axes.
Knifes and daggersEdit
Assassins knifeEditAn assassin uses a knife in an attempt to kill Bran Stark. Its blade is made from Valyrian steel and it belonged to Peter Baelish before he lost it to Tyrion Lannister in a bet.
Eddard Stark's daggerEdit
Like most noblemen Eddard Stark carries a dagger alongside his sword. He uses it to kill Lady, the direwolf of Sansa.
Jaime Lannister's daggerEdit
Jaime carries a dagger alongside his sword when he attacks Lord Eddard Stark in front of the brothel of Ser Petyr Baelish. He uses it to kill Ser Yori Cassel.
In the Free City of Pentos the Unsullied guarding Illyrio Mopatis carry spears formed like a halfmoon.
Most common soldiers are seen with spears and sometimes with the banner of their houses attached to them.
In the Tourney of The Hand Ser Gregor Clegane "The Mountain", Ser Hugh Of The Vale and Ser Loras Tyrell are using jousting lances.